Previous Year Paper
CAT2003Previous Years Paper
There are 12 towns grouped into four zones with three towns per zone. It is intended to connect the towns with a telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required?
A  72 
B  90 
C  96 
D  144

Consider the first zone. The number of telephone lines can be shown a follows.
Therefore, the total number of lines required for internal connections in each zone = 9 × 4 = 36 lines.
Now, consider the connection between any two zones.
Each town in the first zone can be connected to the three towns in the second zone.
Therefore, the lines required = 3 × 3 = 9
Therefore, the total number of lines required for connecting the towns of different zones
= ^{4}C_{2}× 9 = 6 × 9 = 54.
Therefore, the total number of lines in all
= 54 + 36 = 90
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